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Simplifying 12x + 7 = 21x2 Reorder the terms: 7 + 12x = 21x2 Solving 7 + 12x = 21x2 Solving for variable 'x'. Combine like terms: 21x2 + -21x2 = 0 7 + 12x + -21x2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.3333333333 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5714285714x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5714285714x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.3333333333 -0.5714285714x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5714285714x + x2 = 0.3333333333 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.3333333333 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.3333333333 + 0.08163265305 Combine like terms: 0.3333333333 + 0.08163265305 = 0.41496598635 0.08163265305 + -0.5714285714x + x2 = 0.41496598635 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.41496598635 Calculate the square root of the right side: 0.644178536 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.644178536 and -0.644178536.Subproblem 1
x + -0.2857142857 = 0.644178536 Simplifying x + -0.2857142857 = 0.644178536 Reorder the terms: -0.2857142857 + x = 0.644178536 Solving -0.2857142857 + x = 0.644178536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.644178536 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.644178536 + 0.2857142857 x = 0.644178536 + 0.2857142857 Combine like terms: 0.644178536 + 0.2857142857 = 0.9298928217 x = 0.9298928217 Simplifying x = 0.9298928217Subproblem 2
x + -0.2857142857 = -0.644178536 Simplifying x + -0.2857142857 = -0.644178536 Reorder the terms: -0.2857142857 + x = -0.644178536 Solving -0.2857142857 + x = -0.644178536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.644178536 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.644178536 + 0.2857142857 x = -0.644178536 + 0.2857142857 Combine like terms: -0.644178536 + 0.2857142857 = -0.3584642503 x = -0.3584642503 Simplifying x = -0.3584642503Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9298928217, -0.3584642503}
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